Simplify the following expression: $ q = \dfrac{-4}{9} - \dfrac{x + 6}{9x - 3} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9x - 3}{9x - 3}$ $ \dfrac{-4}{9} \times \dfrac{9x - 3}{9x - 3} = \dfrac{-36x + 12}{81x - 27} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{x + 6}{9x - 3} \times \dfrac{9}{9} = \dfrac{9x + 54}{81x - 27} $ Therefore $ q = \dfrac{-36x + 12}{81x - 27} - \dfrac{9x + 54}{81x - 27} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-36x + 12 - (9x + 54) }{81x - 27} $ Distribute the negative sign: $q = \dfrac{-36x + 12 - 9x - 54}{81x - 27}$ $q = \dfrac{-45x - 42}{81x - 27}$ Simplify the expression by dividing the numerator and denominator by 3: $q = \dfrac{-15x - 14}{27x - 9}$